Answer:
Weight of dried bananas = 34.75 kg
Weight of dried apricot = 15.25 kg
Step-by-step explanation:
Given that:
Cost of dried bananas = $4.59 per kg
Cost of dried apricots = $6.59 per kg
Total weight of mixture = 50 kg
Sales price of dried fruit = $5.20 per kg
To find:
The weight of each type of dry fruit = ?
Solution:
Let weight of dried bananas = [tex]x[/tex] kg
Let weight of dried apricot = [tex]y[/tex] kg
[tex]x+y=50 ...... (1)[/tex]
Total cost of dried bananas = Cost of dried bananas per kg multiplied by weight of dried bananas
Total cost of dried bananas = $4.59[tex]x[/tex]
Total cost of dried apricots = Cost of dried apricots per kg multiplied by weight of dried apricots
Total cost of dried apricots = $6.59[tex]y[/tex]
As per question statement,
Total cost of dry fruits = $5.20 [tex]\times[/tex] 50 = $260
[tex]260 = 4.59x+6.59y......(2)[/tex]
Using substitution:
By equation (1):
[tex]x = 50-y[/tex]
Putting in equation (2):
[tex]260 = 4.59 (50-y)+6.59y\\\Rightarrow 2y = 260 - 229.5\\\Rightarrow y = 15.25\ kg[/tex]
[tex]x = 50 - 15.25\\\Rightarrow x = 34.75\ kg[/tex]
Therefore, the answer is:
Weight of dried bananas = 34.75 kg
Weight of dried apricot = 15.25 kg
